Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Butcher_group> ?p ?o }
- Butcher_group abstract "In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field. It was Cayley (1857), prompted by the work of Sylvester on change of variables in differential calculus, who first noted that the derivatives of a composition of functions can be conveniently expressed in terms of rooted trees and their combinatorics. Connes & Kreimer (1999) pointed out that the Butcher group is the group of characters of the Hopf algebra of rooted trees that had arisen independently in their own work on renormalization in quantum field theory and Connes' work with Moscovici on local index theorems. This Hopf algebra, often called the Connes-Kreimer algebra, is essentially equivalent to the Butcher group, since its dual can be identified with the universal enveloping algebra of the Lie algebra of the Butcher group. As they commented:".
- Butcher_group thumbnail Caylrich-first-trees.png?width=300.
- Butcher_group wikiPageExternalLink renormalisation.pdf.
- Butcher_group wikiPageExternalLink journal-03.pdf.
- Butcher_group wikiPageID "23338010".
- Butcher_group wikiPageLength "23106".
- Butcher_group wikiPageOutDegree "67".
- Butcher_group wikiPageRevisionID "637103057".
- Butcher_group wikiPageWikiLink Alain_Connes.
- Butcher_group wikiPageWikiLink Annals_of_Mathematics.
- Butcher_group wikiPageWikiLink Antipode_(algebra).
- Butcher_group wikiPageWikiLink Atiyah–Singer_index_theorem.
- Butcher_group wikiPageWikiLink Augmentation_ideal.
- Butcher_group wikiPageWikiLink Automorphism.
- Butcher_group wikiPageWikiLink Beta-function.
- Butcher_group wikiPageWikiLink Beta_function_(physics).
- Butcher_group wikiPageWikiLink Category:Combinatorics.
- Butcher_group wikiPageWikiLink Category:Hopf_algebras.
- Butcher_group wikiPageWikiLink Category:Numerical_analysis.
- Butcher_group wikiPageWikiLink Category:Quantum_field_theory.
- Butcher_group wikiPageWikiLink Category:Renormalization_group.
- Butcher_group wikiPageWikiLink Coalgebra.
- Butcher_group wikiPageWikiLink Comultiplication.
- Butcher_group wikiPageWikiLink Counit.
- Butcher_group wikiPageWikiLink Derivation_(abstract_algebra).
- Butcher_group wikiPageWikiLink Derivation_(differential_algebra).
- Butcher_group wikiPageWikiLink Differential_calculus.
- Butcher_group wikiPageWikiLink Dimensional_regularization.
- Butcher_group wikiPageWikiLink Dirk_Kreimer.
- Butcher_group wikiPageWikiLink Equivalence_class.
- Butcher_group wikiPageWikiLink Faxc3xa0_di_Brunos_formula.
- Butcher_group wikiPageWikiLink Feynman_diagram.
- Butcher_group wikiPageWikiLink Formal_group.
- Butcher_group wikiPageWikiLink Formal_power_series.
- Butcher_group wikiPageWikiLink Gamma_function.
- Butcher_group wikiPageWikiLink Graph_theory.
- Butcher_group wikiPageWikiLink Group_(mathematics).
- Butcher_group wikiPageWikiLink Henri_Moscovici.
- Butcher_group wikiPageWikiLink Holomorphic_function.
- Butcher_group wikiPageWikiLink Hopf_algebra.
- Butcher_group wikiPageWikiLink Index_theorem.
- Butcher_group wikiPageWikiLink James_Joseph_Sylvester.
- Butcher_group wikiPageWikiLink John_C._Butcher.
- Butcher_group wikiPageWikiLink Laurent_series.
- Butcher_group wikiPageWikiLink Letters_in_Mathematical_Physics.
- Butcher_group wikiPageWikiLink Lie_algebra.
- Butcher_group wikiPageWikiLink Mathematics.
- Butcher_group wikiPageWikiLink Milnor–Moore_theorem.
- Butcher_group wikiPageWikiLink Minimal_subtraction_scheme.
- Butcher_group wikiPageWikiLink Numerical_analysis.
- Butcher_group wikiPageWikiLink Ordinary_differential_equation.
- Butcher_group wikiPageWikiLink Philosophical_Magazine.
- Butcher_group wikiPageWikiLink Polynomial.
- Butcher_group wikiPageWikiLink Polynomial_ring.
- Butcher_group wikiPageWikiLink Power_series.
- Butcher_group wikiPageWikiLink Quantum_field_theory.
- Butcher_group wikiPageWikiLink Renormalization.
- Butcher_group wikiPageWikiLink Renormalization_group.
- Butcher_group wikiPageWikiLink Riemann_sphere.
- Butcher_group wikiPageWikiLink Riemann–Hilbert_problem.
- Butcher_group wikiPageWikiLink Rooted_tree.
- Butcher_group wikiPageWikiLink Rota-Baxter_algebra.
- Butcher_group wikiPageWikiLink Rota–Baxter_algebra.
- Butcher_group wikiPageWikiLink Runge-Kutta_method.
- Butcher_group wikiPageWikiLink Runge–Kutta_method.
- Butcher_group wikiPageWikiLink Runge–Kutta_methods.
- Butcher_group wikiPageWikiLink Symmetry_group.
- Butcher_group wikiPageWikiLink Séminaire_Bourbaki.
- Butcher_group wikiPageWikiLink Séminaire_Nicolas_Bourbaki.
- Butcher_group wikiPageWikiLink Tree_(graph_theory).
- Butcher_group wikiPageWikiLink Universal_enveloping_algebra.
- Butcher_group wikiPageWikiLink Vector_field.
- Butcher_group wikiPageWikiLink File:Caylrich-first-trees.png.
- Butcher_group wikiPageWikiLinkText "B-series".
- Butcher_group wikiPageWikiLinkText "Butcher group".
- Butcher_group hasPhotoCollection Butcher_group.
- Butcher_group wikiPageUsesTemplate Template:Citation.
- Butcher_group wikiPageUsesTemplate Template:Cquote.
- Butcher_group wikiPageUsesTemplate Template:Harvtxt.
- Butcher_group wikiPageUsesTemplate Template:Reflist.
- Butcher_group subject Category:Combinatorics.
- Butcher_group subject Category:Hopf_algebras.
- Butcher_group subject Category:Numerical_analysis.
- Butcher_group subject Category:Quantum_field_theory.
- Butcher_group subject Category:Renormalization_group.
- Butcher_group hypernym Group.
- Butcher_group type Band.
- Butcher_group type Algebra.
- Butcher_group type Algorithm.
- Butcher_group type Combinatoric.
- Butcher_group type Field.
- Butcher_group type Mechanic.
- Butcher_group type Physic.
- Butcher_group comment "In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field.".
- Butcher_group label "Butcher group".
- Butcher_group sameAs m.06w5q7x.
- Butcher_group sameAs Q5002457.
- Butcher_group sameAs Q5002457.
- Butcher_group wasDerivedFrom Butcher_group?oldid=637103057.
- Butcher_group depiction Caylrich-first-trees.png.